The R3-carbon allotrope: a pathway towards glassy carbon under high SUBJECT AREAS: MECHANICAL pressure PROPERTIES ELECTRONIC MATERIALS Xue Jiang1,2, Cecilia A˚ rhammar3, Peng Liu1, Jijun Zhao2 & Rajeev Ahuja1,4 STRUCTURE OF SOLIDS AND LIQUIDS 1Department of Materials and Engineering, Royal Institute of Technology, 10044 Stockholm, Sweden, 2Key Laboratory of Materials ELECTRONIC STRUCTURE Modification by Laser, Ion and Electron Beams Dalian University of Technology, Ministry of Education, Dalian 116024, China, 3Sandvik Coromant, Lerkrogsv. 13, S-126 80 Stockholm, Sweden, 4Department of Physics and Astronomy, Box 516, Uppsala University, 75120, Uppsala, Sweden. Received 8 November 2012 Pressure-induced bond type switching and phase transformation in glassy carbon (GC) has been simulated Accepted by means of Density Functional Theory (DFT) calculations and the Stochastic Quenching method (SQ) in a 25 April 2013 wide range of pressures (0–79 GPa). Under pressure, the GC experiences a hardening transition from sp- and sp2-type to sp3-type bonding, in agreement with previous experimental results. Moreover, a new Published crystalline carbon allotrope possessing R3 symmetry (R3-carbon) is predicted using the stochastic SQ 23 May 2013 method. The results indicate that R3-carbon can be regarded as an allotrope similar to that of amorphous GC. A very small difference in the heat of formation and the coherence of the radial and angular distribution functions of GC and the R3-carbon structure imply that small perturbations to this crystalline carbon Correspondence and allotrope may provide another possible amorphization pathway of carbon besides that of quenching the liquid melt or gas by ultra-fast cooling. requests for materials should be addressed to J.Z. ([email protected]. arbon is an intriguing element for scientists from many fields because of the diverse sp, sp2 and sp3 bonding cn) or R.A. (rajeev. states and its fascinating physical and chemical properties1. Within condensed matter physics, there are [email protected]) many well-known carbon allotropes, namely; graphite, fullerene, graphene, nanotubes, diamond and C 2–4 amorphous carbon . Motivated by the supreme properties and potential applications of those carbon structures, there is great interest in synthesizing new allotropes. The term glassy carbon (GC) includes numerous modifications of carbon with different fraction of sp, sp2 and sp3 hybridized states from short-range to intermediate-range-order structures. Many of these modifications are used within industrial applications where their unique properties are utilized. Combining the chemical inertness of a glass with the high electrical conductivity of a ceramic, GC finds important applications in the manufacturing of crucibles and electrodes and as coatings for electronic devices. One commonly used thin film form of glassy carbon is the diamond like carbon coating, which is well used as a protective wear resistant coating. Within this group of glassy carbon coatings, some contain about 50 at.% hydrogen (a-C:H), other contain less than 1% hydrogen (a-C)5. The a-C:H typically contain sp3 fractions smaller than 50%, while the a-C films can contain 85% or more sp3 bonds5. Many different structures of glassy carbon have been suggested on the basis of X-ray Diffraction (XRD)- measurements and the high resolution transmission electron microscopy imaging4. Ergun and Tiensuu2 found both sp2 and sp3 C-C bonds in glassy carbon. Jenkins3 considered the GC crystallite as a complex polymer-like structure, where graphite-like layers were stacked together. The model of glassy carbon with carbyne-like chains has also been proposed by Pesin et al.5. Recently, a model for the structure of glassy carbon at high and low temperature have gained acceptance6. The high temperature structure can be thought of as mainly consisting of broken or imperfect fullerene-like multilayered nanoparticles with very large enclosed pores. The low temper- ature structure consists of a curved carbon sheet consisting of pentagons, heptagons and hexagons. The transformation mechanism amongst various forms of carbon allotropes and the unrevealed metastable phases along these transition pathways have been a long-lasting issue, since these polymorphs possess entirely different electronic and mechanical properties. Cold compression with diamond anvil cell (DAC) and first- principles simulations are regarded as the most powerful experimental and theoretical tools to interpret the process of conversion7. At hydrostatic pressure up to 5 GPa, many experiments reveal a fascinating phase transformation of fullerenes into ordered or disordered diamond or graphite8, in which the hardness sometimes SCIENTIFIC REPORTS | 3 : 1877 | DOI: 10.1038/srep01877 1 www.nature.com/scientificreports can approach that of perfect sp3-type diamond. Moreover, the com- pression behavior, the phase diagram, the optical, electronic, and mechanical properties of the C60 crystal have been well investigated in the past decade9. By means of cold compression of graphite at ambient temperature, Mao et al.7 observed partial sp2-type bonds conversion into sp3-type bonds in graphite at around 14 GPa, which demonstrated the formation of a new superhard phase instead of the hexagonal and cubic diamonds. Theoretical studies have proposed several possible structures for such cold compressed graphite, includ- ing the monoclinic M carbon10, body centered tetragonal Bct-C4 carbon11, orthorhombic W carbon12, R carbon, P carbon13, and Cco-C8 carbon14. The XRD-patterns of those predicted structures showed a rough agreement with the corresponding experimental results, However, M-Carbon has been recently supported again by experiment15. With the aid of high temperature (T 5 2300–2500 K), graphite converts completely into diamond at pressures above 15 GPa16,17. Very recently, Lin et al.18 observed a new carbon allo- trope with a fully sp3-bonded amorphous structure formed from GC Figure 1 | The cohesive energies and symmetries of twenty random carbon structures with the densities of graphite (2.24 g/cm3) and after hydrostatic loading of more than 40 GPa at room temperature. 3 Using synchrotron X-ray Raman spectroscopy, they found a con- diamond (3.52 g/cm ), respectively. tinuous pressure-induced sp2-to-sp3 structural change. This new GC allotrope was suggested to be a superhard material, as indicated by its of R3, it is clear that the R3-structure has its main peaks at 24.1 and exceptional yield strength up to 130 GPa with a confining pressure of 36.4 degrees 2h, angles at which no other of the compressed graphite 60 GPa. Yet the exact glassy carbon structures during phase trans- phases display any diffracted peaks. Moreover, all other carbon allo- ition and the origin of its superior mechanical properties has not tropes display main peaks between 40 and 45 degrees 2h, whereas been explained. R3-carbon completely lacks intensity in this region. In this paper, we explore the detailed structures of GC and illus- In order to investigate the dynamical stability of the R3-phase, trate its mechanical properties under a wide pressure range of 0– phonon dispersion relationships have been calculated by Density 79 GPa by means of DFT. The initial GC model at ambient pressure Functional Perturbation Theory (DFPT) and the code of Phonopy was built by the stochastic quenching (SQ) method19–23 where the (Fig. 3). The Brilliouin zone of this allotrope is complex due to its low density and minimum number of carbon atoms were tested carefully. symmetry and therefore phonon frequencies along paths in all three Our results provide theoretical evidence of a change in bonding type directions in space were studied (G-A-H-K-G-M-L-H). From the (sp, sp2, and sp3) of the GC-structures under high pressure. A certain calculated phonon spectrum it is clear that there are no negative amount of the C2 dimer was found in the glassy carbon structures, frequencies throughout the entire Brilliouin zone, which confirms independently of the loading pressure but decreasing with annealing that the R3-phase is dynamically stable. 2 3 temperature. The existence of the C2-dimer may delay the sp -sp We first performed benchmark testing of the SQ method for a 4- transformation. More strikingly, we predict a new carbon crystalline atoms and a 8-atoms cell with densities of 2.24 g/cm3 and 3.52 g/cm3, phase which can be triggered to transform into the amorphous state respectively, corresponding to the density of graphite and diamond. by exerting a small perturbation to the system. It can be regarded as To assess the accuracy of our first-principles total energy methods, we the embryo of GC and may provide an alternate method of amor- calculated the lattice constants and cohesive energies of diamond and phization of the carbon phase besides quenching from liquid melt or graphite crystals using three exchange correlation functionals: the gas by ultra-fast cooling. Perdew-Becke-Ernzerhof functional for solids and surfaces (PBEsol), a density functional constructed with a long-range disper- Results sion correction (D2)25 and the van der Waals density functional 26 Figure 1 shows the cohesive energies and symmetries of twenty ran- (vdW-DF) . In the bulk calculations, the Brillouin zone was sampled dom structures generated by the SQ method. Clearly, these twenty by a 10 3 10 3 10 k points mesh. The computed results are com- structures cover many different atomic arrangement and symmet- pared with experimental values in Table I. For the lattice constants, ries. As already demonstrated in our previous work24, the SQ method the results of DFT-D2 method shows best agreement with the experi- efficiently reproduces metastable phases that may only be found mental values, while the vdW-DF method yields the largest error bars. experimentally by ultrafast cooling from liquid melt or by off- This sequence is completely opposite for the cohesive energy, where equilibrium synthesis. In addition, beyond the previously reported the error decreases in the order DFT-D2, DFT/PBEsol and vdW-DF.